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Correlations and functional connections in a population of grid cells.

Dunn B, Mørreaunet M, Roudi Y - PLoS Comput. Biol. (2015)

Bottom Line: We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs.The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module.Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.

View Article: PubMed Central - PubMed

Affiliation: Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU, Trondheim, Norway.

ABSTRACT
We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.

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Theta clusters.Preferred phase of theta of the 27 cells in data set 1 plotted onto the unit circle. The cells were clustered into two groups (red and blue) (see Material and Methods). Asterisks mark cluster centers.
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pcbi.1004052.g010: Theta clusters.Preferred phase of theta of the 27 cells in data set 1 plotted onto the unit circle. The cells were clustered into two groups (red and blue) (see Material and Methods). Asterisks mark cluster centers.

Mentions: The cells could be divided in two clusters based on preferred phase of theta. The theta phase preference was defined as the peak in a circular kernel smoothed density estimate of the distribution of theta value at spike time. The number of clusters were defined as the number of local peaks in a kernel smoothed density estimate of the distribution of theta phase preference peaks for all cells. A circular k-means clustering algorithm were performed to assign cells to clusters. The clusters are shown in Fig. 10.


Correlations and functional connections in a population of grid cells.

Dunn B, Mørreaunet M, Roudi Y - PLoS Comput. Biol. (2015)

Theta clusters.Preferred phase of theta of the 27 cells in data set 1 plotted onto the unit circle. The cells were clustered into two groups (red and blue) (see Material and Methods). Asterisks mark cluster centers.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4340907&req=5

pcbi.1004052.g010: Theta clusters.Preferred phase of theta of the 27 cells in data set 1 plotted onto the unit circle. The cells were clustered into two groups (red and blue) (see Material and Methods). Asterisks mark cluster centers.
Mentions: The cells could be divided in two clusters based on preferred phase of theta. The theta phase preference was defined as the peak in a circular kernel smoothed density estimate of the distribution of theta value at spike time. The number of clusters were defined as the number of local peaks in a kernel smoothed density estimate of the distribution of theta phase preference peaks for all cells. A circular k-means clustering algorithm were performed to assign cells to clusters. The clusters are shown in Fig. 10.

Bottom Line: We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs.The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module.Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.

View Article: PubMed Central - PubMed

Affiliation: Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU, Trondheim, Norway.

ABSTRACT
We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.

Show MeSH
Related in: MedlinePlus